Skip to main content
Ch. 3 - Probability
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLarson 8th EditionCh. 3 - ProbabilityProblema 3.4.12
Capitolo 3, Problema 3.4.12

In Exercises 7-14, perform the indicated calculation.
12. (10C7)/(14C7)

Guida verificata passo dopo passo
1
Step 1: Understand the problem. The problem involves calculating a ratio of combinations. Specifically, we need to compute \( \frac{{10C7}}{{14C7}} \), where \( nCk \) represents the number of combinations of \( k \) items chosen from \( n \) items.
Step 2: Recall the formula for combinations. The formula for \( nCk \) is given by \( nCk = \frac{{n!}}{{k!(n-k)!}} \), where \( n! \) is the factorial of \( n \).
Step 3: Apply the formula to calculate \( 10C7 \). Substitute \( n = 10 \) and \( k = 7 \) into the formula: \( 10C7 = \frac{{10!}}{{7!(10-7)!}} = \frac{{10!}}{{7! \cdot 3!}} \).
Step 4: Apply the formula to calculate \( 14C7 \). Substitute \( n = 14 \) and \( k = 7 \) into the formula: \( 14C7 = \frac{{14!}}{{7!(14-7)!}} = \frac{{14!}}{{7! \cdot 7!}} \).
Step 5: Simplify the ratio \( \frac{{10C7}}{{14C7}} \). Substitute the expressions for \( 10C7 \) and \( 14C7 \) into the ratio and simplify by canceling common terms. This will give the final result.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
4m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Combinations

Combinations refer to the selection of items from a larger set where the order of selection does not matter. The notation 'nCr' represents the number of ways to choose 'r' items from 'n' items, calculated using the formula n! / (r!(n-r)!), where '!' denotes factorial. Understanding combinations is essential for solving problems involving groups or selections.
Video consigliato:
Percorso guidato
05:22
Combinations

Factorial

A factorial, denoted as 'n!', is the product of all positive integers up to 'n'. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials are fundamental in combinatorial calculations, as they help determine the total arrangements or selections of items, making them crucial for understanding combinations.
Video consigliato:
Percorso guidato
05:22
Combinations

Ratio of Combinations

The ratio of combinations compares two different combinations, providing insight into their relative sizes. In the expression (10C7)/(14C7), it calculates how many ways you can choose 7 items from 10 compared to choosing 7 from 14. This concept is useful in probability and statistics for understanding the likelihood of different outcomes.
Video consigliato:
Percorso guidato
05:22
Combinations
Pratica correlata
Domanda del libro di testo

Matching Probabilities In Exercises 11-16, match the event with its probability.

a. 0.95

b. 0.005

c. 0.25

d. 0

e. 0.375

f. 0.5

16. You toss a coin four times. What is the probability of tossing tails exactly half of the time?

135
views
Domanda del libro di testo

Warehouse In Exercises 51-54, a warehouse employs 24 workers on first shift, 17 workers on second shift, and 13 workers on third shift. Eight workers are chosen at random to be

interviewed about the work environment.

Find the probability of choosing four third-shift workers.

125
views
Domanda del libro di testo

80. Unusual Events Can any of the events in Exercises 75-78 be considered unusual? Explain.

134
views
Domanda del libro di testo

29. Explain, in your own words, why in the Addition Rule for P(A or B or C), P(A and B and C) is added at the end of the formula.

292
views
Domanda del libro di testo

23. Footrace There are 72 runners in a 10-kilometer race. How many ways can the runners finish first, second, and third?

116
views
Domanda del libro di testo

"Identifying Simple Events In Exercises 33-36, determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning.

36. You randomly select one card from a standard deck of 52 playing cards. Event B is selecting the ace of spades."

62
views